1. Crystal-Air surface Interphase boundary Grain boundary Twin Boundary Stacking Faults Crystal Boundary Crystal-Crystal Low angle High angle 2D DEFECTS (Surface / Interface) Anti-phase Boundary

2. Homophase Low angle High angle Based on axis Based on angle of rotation Based on Lattice Models Twist Tilt Mixed Special Random CSL/Other Based on Geometry of the Boundary plane Curved Faceted Mixed

4. Picture ARM-UC Berkeley4 Curtesy S. Van Tenderloo

5. Interphase Low angle High angle Based on axis Based on angle of rotation Based on Lattice Models Twist Tilt Mixed Special Random Epitaxial/Coherent Based on Geometry of the Boundary plane Curved Faceted Mixed Semicoherent Incoherent Wulff-type constructions

6. Coherence at interfaces Coherent interface means an interface in which the atoms match up on a 1-to-1 basis (even if some elastic strain is present). Incoherent interface means an interface in which the atomic structure is disordered. Semi-coherent interface means an interface in which the atoms match up, but only on a local basis, with defects (dislocations) in between.

7. Coherent interfaces Coherent interface means an interface in which the atoms match up on a 1-to-1 basis (even if some elastic strain is present). Near identical lattice parameters, often thin layers of A on B

8. Incoherent interfaces Incoherent interface means an interface in which the atomic structure is disordered. General case, analogous to a general high-angle grain boundary (roughly)

9. Semi-coherent interfaces Semi-coherent interface means an interface in which the atoms match up, but only on a local basis, with defects (dislocations) in between. Comparable to a low-angle grain boundary with a dislocation array (now called misfit dislocations)

10. Epitaxy Britannica Concise Encyclopedia:Britannica Concise Encyclopedia: epitaxy Process of growing a crystal of a particular orientation on top of another crystal. If both crystals are of the same material, the process is known as homoepitaxy; if the materials are different, it is known as heteroepitaxy. Common types of epitaxy include vapour phase, liquid phase, and solid phase, according to the source of the atoms being arranged on the substrate. Comment 1: “growth” is not needed here… Comment 2: often used more generally than this

11. Main Types of Epitaxy Homoepitaxy –Growth of material on the same substrate (Si on Si) Pseudomorphic growth –Material adopts the lattice of substrate/matrix Coincidence –Material has certain spacings common with substrate/matrix –Similar to CSL Cube-Cube –Major orientations are parallel, e.g. [001] A //[001] substrate

12. Heteroepitaxial growth modes Frank-van der Merwe 1 2 layer-by-layer Volmer-Weber trade surface for interface Stranski-Krastanov relieve stress

13. Pseudomorphic Growth

14. Consider a layer of “A” on “B”, of thickness t Take z normal to film, x in plane Suppose that lattice of A is larger than that of B, and would match that of B is strained by e xx along x Strain energy scales as te xx 2 (I leave to you to work this out in detail…) per unit area

15. Interface Energy If A matches the lattice of B, the “bonding” will be good Energy of interface per unit area is  AB Total energy of system –E = t*e xx 2 +  AB

16. Hetero epitaxial growth (“lattice-mismatched” growth) permits the fabrication of dissimilar materials on the same substrate Strain in the growing film depends on thickness and mismatch Thin layer - the film will elastically deform to match the in-plane lattice parameter of the substrate Thick layer - film will revert to its unstrained lattice parameter, with misfit dislocations at the interface with the substrate Alternative

18. Alternative, dislocations Put dislocations at the interfaces of Burgers vector b, separation L Assume that these remove all the strain –b/L = e xx Energy of dislocations per unit area will scale as b 2 /L (better, use Read-Shockley model or similar, Frank-Van Der Merwe) –Note: no t dependence TT T T

19. Energy Balance For “phase transition” pseudomorphic to dislocations  E = -C 1 *t*e xx 2 + C 2 (b 2 /L)

20. Dislocation Standoff TT T T 11 22 TT T T  1 >  2 TT T T  1 <  2  1 =  2 Dislocation energy scales with shear modulus

21. Energy Balance Better, consider a half dislocation loop growing in (kinetics) Energy of loop =  RC 2 b 2 Strain energy relieved = C 1  R 2 /2e xx 2 For transition (remove  & 1/2 )  E = -C 1 R 2 e xx 2 + RC 2 b 2 R

22. Classic Nucleation Problem

23. Islands

24. Similar Cases Thin films/precipitates can have different structures –Energy for phase change < interface energy  E = C 1 *V + C 2 V 2/3 (  A -  B ) 3 nm VN B1-AlN Figure 3

25. Epitaxial Stabilization of B1-AlN in AlN/VN Superlattices a VN Energy of B1-AlN and zb-AlN vs. underlayer lattice constant (not including the interfacial energy). [Madan et al.] zb-AlNB1-AlNw-AlN Al N

26. Similar Cases Nanoparticles can have different structures –Energy for elastic strain < surface energy  E = C 1 *V + (C A -C B ) V 2/3  A

27. Stranski-Krastanow Growth Formation of 3D structures (q-dots) preceded by wetting layer Relieve strain energy, increase surface energy  E = C 1 V 2/3 +C 2 V

28. Comments Similar to CSL boundaries, one can have dislocations of the coherency between the two materials at an interface A step at the interface is normally a different type of dislocation – sessile (immobile) There is more….

29. Interphase Low angle High angle Based on axis Based on angle of rotation Based on Lattice Models Twist Tilt Mixed Special Random Epitaxial/Coherent Based on Geometry of the Boundary plane Curved Faceted Mixed Semicoherent Incoherent Wulff-type constructions

30. Picture ARM-UC Berkeley30 Curtesy S. Van Tenderloo